Is Illustrator really the most suited tool to draw a (fairly simple) map from scratch and print it on a flyer? Are there any other tools or apps out there that might make this task easier?
There are actually online tools that can do this. However, personally, I would start out with a google map screenshot and work from that - in Illustrator.
You could take a round on the net and search for brushes and plugins for Illustrator that have ready-made map-elements. Here is but one example of what you can find: symbols ready made. Such as:
These post might also be helpful to you:
QGIS (http://qgis.org/en/site/) has a PDF export function, but it isn't exactly easy by any stretch of the imagination, as it's a full GIS program, but can export to PDF. You can pull in OpenStreetMaps data as well. Open-source, free.
Here's a good tutorial: http://multimedia.journalism.berkeley.edu/tutorials/qgis-basics-journalists/
Inkscape is another open source program you could use. But as others have suggested I would personally stick with Illustrator. Instead of grabbing a screenshot of a map you could start with a vector file instead.
Take a look at this website I created. http://openvectormaps.com